Radamel Falcao had given Atletico the lead although that was cancelled out by a Mame Biram Diouf strike.
Nonetheless, a late Eduardo Salvio goal grabbed a vital one-goal lead for the La Liga side heading into next week's return leg, but Simeone insists his side still have plenty of work to do.
"If I were a fan of Hannover, I would be happy with the result," Simeone said in his post-match press conference.
"They [Hannover] will have the full support of their fans in Germany and the goal gives them a chance.
"At the end of the match we aren't in the comfortable position that we deserve to be," he said. "In the first half we started well and could have scored a second, but then our level started to drop.
"They scored with their first chance and we couldn't find the goal that would have settled us down.
"In the second half the team had a lot of heart and strength and although we lacked a little bit of clarity in the final third we were still just winners."
"They scored their goal at the first chance. The result is what it is, there is nothing we can do about it, but we deserved to win."
The Argentine tactician was also pleased with the way his players managed to bounce back from last weekend's 1-0 La Liga loss to Real Zaragoza.
"Our morale was good," Simeone added. "We have been competitive in every match we have played, whether we have won or lost."
Hannover boss Mirko Slomka also admitted that Atleti had deserved the victory on the balance of play but was disappointed to lose a goal so late on.
He said: "You never accept a defeat but we have to be aware that we still have a chance to change things at home. It was a deserved result because Atletico had many more chances but it hurts to lose a goal in the final minutes."
Slomka is hoping his side can improve for the return in northern Germany next week, but believes the Spaniards are favourites to progress.
He said: "We have to be stronger, play more offensively and obviously win in the second leg but Atletico have more experience, very good players and they remain the favourites."
"We need our fans in the second leg and then we could do it," he said on his club's website.
"We are strong at home. It is not over yet by a long way, but Atletico are favourites.
"It is frustrating when you lose so late on. But we got the away goal and that is important."
Atletico are not taking the task in Hannover lightly either, with their attacking midfielder Diego - who previously played for both Werder Bremen and Wolfsburg in the Bundesliga - warning against being too confident.
"Hannover are a compact team and the return leg is going to be difficult for us," he said.
"We have a small advantage to take with us to Germany, but it will be tough.
"Hannover are very patient and they are very good on the counter-attack. We are going to have to be careful since they will be stronger at home than they were here."
Atletico next play Getafe in the league on Sunday.